Question: Subtract $8y^2-5y+7$ from $2y^2+7y+11$.
Since we are asked to subtract $8y^2-5y+7$ from $2y^2+7y+11$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $10$ from $6$ ", we would rewrite it as $6 - 10$. In other words, we would start with $6$ and then subtract $10$. Let's use this pattern to rewrite the problem as one expression: ${(2y^2+7y+11)-(8y^2-5y+7)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(2y^2+7y+11){-}(8y^2-5y+7)\\ \\ =&(2y^2+7y+11){-}8y^2{-}(-5y){-}7\\ \\ =&2y^2+7y+11-8y^2+5y-7 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${y^2}, {y},$ and the $\text{{constant}}$ term: ${{2y^2} {+7y} {+11} {-8y^2} {+5y} {-7}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(2-8)y^2} + {(7+5)y} + {(11-7)}}$ When we combine the coefficients in front of each term, we get the following trinomial: $-6y^2 +12y+4$